Residual stress distribution as a function of depth in graphite/copper brazing joints via X-ray diffraction

1. Introduction

In recent years, there has been an increasing interest in Carbon materials [[1], [2], [3], [4], [5], [6], [7]]. Graphite is one of the most commonly used carbon materials in many aspects such as vehicle manufacturing [8] and fusion reactors [9,10]. It is often selected as the material for plasma facing components [11,12] in fusion reactors due to its high thermal conductivity and outstanding thermal shock resistance. Copper is often chosen as the sink material [13,14] for the fusion reactors because of its excellent electrical and thermal conductivity. Thus there is an urgent need [15] for the joining of graphite and copper, and plenty of research has been performed. Active metal brazing [[16], [17], [18], [19], [20], [21]] which incorporates active alloying elements such as the Ti, Zr and Hf into the brazing filler has become one of the most promising methods to join graphite with copper because this method is suitable for complex structures and large joining area. However, due to the significant difference in the coefficient of thermal expansion (CTE) between graphite (4.8 × 10^-6 °C^-1) and copper (16.7 × 10^-6 °C^-1), high level of residual stress can be generated in the joint, which is detrimental to the reliability of the joint and sometimes can cause the direct failure of the joint. The failure of the joint in fusion reactors will expose the metal part to the plasma environment and lead to catastrophic results. Thus plenty of research has been carried out to reduce the residual stress in the joint. The most commonly used method is to apply an interlayer inside the joint and the selection of the interlayer is often employed according to at least one of the following criteria: (1) the interlayer should have a relatively low yielding strength such as Cu [22,23] and the residual stress in the joint can be released by the plastic deformation of the ductile interlayer. (2) The CTE of the interlayer is between that of graphite and copper which could form a gradient structure in the joint and moderate the residual stress distribution. For the graphite/ copper brazing joint, Mo interlayer [22] is usually applied for this purpose. Zhou et al. [24] incorporated both types of interlayer into the joint and improvement of the joint strength was observed.

Since the residual stress plays an important role in the reliability of the brazing joint, plenty of research has been carried out to investigate its distribution. Currently, most research regarding the residual stress distribution in the joints is achieved by finite element modelling (FEM) [25]. Zhong et al. [22] predicted the residual stress distribution in a graphite/copper brazing joint with and without Mo/ Cu interlayer. It was found that the insertion of the Mo/Cu interlayer could significantly reduce the residual stress in the joint. However, for the graphite/copper brazing joint, reaction products between substrates and brazing fillers with complex morphology can often be observed. Moreover, graphite usually has a porous microstructure, and the brazing filler is often found to infiltrate into the graphite substrate [26]. These two features are usually not considered when setting up the FE models shown in the previous reports, which could make the modelling results less reliable. Direct measurement of the residual stress distribution in the joint is a more straightforward way which could avoid this problem. However, the measurement of the residual stress distribution in the graphite/ copper brazing joint can be challenging. Since graphite is a kind of material vulnerable to cracks, the commonly used destructive methods for welding joints such as hole drilling and the ring core method [27,28] are not applicable. Raman Spectra is a frequently used method to characterise carbon materials and measure their residual stress [[29], [30], [31]]. However, graphite is not transparent for Raman laser, the residual stress at the interface which is considered to be most relevant to the failure of the joint cannot be achieved via this method. Graphite has a relatively low attenuation coefficient for X-ray ($\frac{μ}{ρ}$=4.576cm²/g $\frac{μ}{ρ}$=4.576cm²/g $\frac{μ}{ρ}$=4.576cm²/g) [32] and X-ray could penetrate through the graphite substrate, which makes it possible to measure the residual stress distribution as a function of depth in the joint by X-ray diffraction (XRD). As far as the authors know, there is no available report for the measurement of the residual stress distribution in the graphite/ copper joint. In this paper, to investigate the effect of the interlayer on the residual stress distribution in graphite/ copper brazing joint, we fabricated three different brazing joints: with no interlayers, with a ductile copper interlayer and with a niobium interlayer which has a CTE between graphite and copper. A method is developed to measure the residual stress distribution as a function of depth by XRD in graphite/ copper brazing joints. The relationship between the residual stress distribution in the joint and the strength and the failure position of the joint is discussed.

2. Experimental

The graphite is fabricated into 3.5 mm × 3.5 mm × 4 mm pieces by a Diamond cutting wheel, and the Cu plate was cut into 10 mm × 10 mm × 1 mm pieces via electrical discharge machining. Prior to the brazing process, the surface roughness of the substrates was grounded to 1 μm, and the substrates were ultrasonically cleaned in acetone for 10 min. The brazing process was carried out in a vacuum furnace at 850 °C for 10 min with a vacuum of 3 × 10^-3 Pa. The cooling rate was set as 10 °C/min to inhibit cracks being generated during the cooling procedure. The applied brazing alloy was the silver-based active brazing alloy of composition (wt%) Ag-27.5Cu-1.0Al-2.5Ti with a thickness of 80 μm, which was fabricated into 3.5 mm × 3.5 mm slices to fit the size of the graphite. The thickness of the copper and niobium interlayer used in this research is 100 μm, and the foils were cut into 3.5 mm × 3.5 mm as well.

The residual stress distribution as a function of depth in the graphite was measured in transmission geometry using XRD (Bruker D8 Advanced) with a Euler cradle, which enabled the sample to be rotated in both ϕ and χ angles (φ denotes the rotation of the specimen around the specimen surface normal and χ is the angle of rotation of the sample around an axis defined by the intersection of the diffraction plane and the sample surface.) [33]. A Göbel mirror in the incident beam was used to achieve a parallelised beam. In this experiment, using the parallelised X-ray beam could help increase the resolution of the measurement comparing to the divergent beam since the interaction volume of the divergent beam will overlap with each other for each step. The size of the beam was adjusted to 1 mm × 1 mm by applying an aperture. A 0.2 mm soller slit was placed before the detector to suppress the peak broadening induced by the geometry. The geometry of the experiment is shown in Fig. 1a). The incident angle was fixed at zero during the measurement, and the beginning of the measurement, the sample was aligned to make the beam grazing incident on the upper surface of the graphite. Then the sample was moved up as a step size of 1 mm making the interaction volume move towards the interface. The residual stress in graphite was measured using the sin²ψ method (ψ is the angle of inclination of the specimen surface normal with respect to the diffraction vector.) [33] and the variation of the ψ angle was realised by altering the χ angle, as shown in Fig. 1a). In total, 6 ψ angles of -30°, -25°, -15°, 15°, 25° and 30° were covered. The peak (002) was chosen to carry out the measurement and the scanning two theta angle ranged from 25.5° to 27.5°. The peak position was determined using the peak fitting function in origin program and the peak shape was found to be a good fit to the Psdvoigt2 function [34]. Since the shape of the joint is symmetric in X and Y directions, the residual stress in Graphite can be regarded as a bi-axial plane stress. Thus, for the sin²ψ sin²ψ sin²ψ method, the relationship between residual stress σ and sin²ψ sin²ψ can be demonstrated as [35]

$\frac{d-d_0}{d_0}=-\frac{1}{2}S_2σsin^2ψ$ (1)

where d is the d-spacing of the plane measured at angle ψ and d0 is the stress free d-spacing. In most circumstance, the value of d0 d0 can be very difficult to be achieved and the d value measured when ψ=0 is used as d0 without causing significant errors. $-\frac{1}{2}S_2$ is the X-ray elastic constant which is calculated from ISODEC [36] and set to 9.286 × 10^-6 MPa^-1. The residual stress can be achieved from the slope between the $\frac{d-d_0}{d_0}$ and $-\frac{1}{2}S_2σsin^2ψ$$-\frac{1}{2}S_2σsin^2ψ$, which is realised by using the linear fitting tool in Origin software.

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Fig. 1.   a) Schematic of the geometry of the residual stress measurement, the parallelised X-ray fully penetrate through the graphite and the diffraction pattern is recorded by the detector, b) schematic of the shear testing of the joint, where the load is applied on the copper substrate.

After residual stress measurement, the same sample was cross sectioned by a Diamond cutting wheel, ground and polished to 1 μm finish. The microstructure of the joint was characterised by Scanning Electron Microscopy (SEM) coupled with Energy-dispersive X-ray spectroscopy (EDS) detector. The strength of the joint was measured by the shear test, the schematic of the testing is shown in Fig. 1b). After the shear test, the phases on the fracture surface of the joint were characterised by XRD and the achieved pattern was refined by the TOPAS program using the Trucano’s model [37] for graphite based on a Hexagonal cell (P63/mmc), the Christensen’s [38], Novgorodova’s [39] and Otte’s [40] models for TiC, Silver and Copper based on cubic models (Fm-3 m).

3. Results and discussion

3.1. Residual stress distribution

As shown in Fig. 1, the residual stress measurement was carried out by transmission geometry. The absorption of the X-ray in a specific material can be calculated by Beer-Lambert law:

$\frac{I}{I_0}=e^{-\frac{μ}{ρ}ρτ}$ (2)

where I₀ I₀ is the original intensity of the X-ray beam, I I is the intensity of the X-ray beam after penetrating the material, $\frac{μ}{ρ}$ $\frac{μ}{ρ}$ is the mass attenuation coefficient of the material to the X-ray with a certain energy, which is 4.576 cm²/g for 8 keV X-ray beam in graphite [32], ρ ρ is the density of the material, which is 2.266 g/cm³ and τ τ is the travelling distance of the X-ray beam in the material. Usually, when $\frac{I}{I_0}$=1% $\frac{I}{I_0}$=1%, the X-ray beam is considered to be fully absorbed. After calculation, the CuK_α X-ray beam is found to be able to penetrate through the graphite with a thickness of $\widetilde{4}$.4 mm, which could help to ensure that the samples used in our experiment can be fully penetrated.

Fig. 2a) shows an example of the peak fitting, from which it can be seen that the peak is generally symmetrical and the full width at half maxima (FWHM) is about 0.38°, which indicates that the application of the 0.2 mm soller slit effectively suppresses the peak broadening induced by the transmission geometry. The peak is found to be well fitted by the Psdvoigt2 model with Adjust R-square of 0.98. Then the linear fitting between $\frac{d-d_0}{d_0}$ $\frac{d-d_0}{d_0}$ and sin²ψ sin²ψ is carried out and one of the fitting results is shown in Fig. 2b). The negative slope indicates that the residual stress in the graphite near the interface is compressive. The residual stress distributions as a function of depth in the graphite of various joints are shown in Fig. 2c). As shown in the figure, the residual stress distributions as a function of depth in all the joints are very similar. The values of the residual stress in all the samples are very small at the surface and become increasingly compressive towards the interface. This observation corresponds well with the previous research. The residual stress distribution in zirconia/iron joints [41] and molybdenum disilicide/stainless steel joints [42] has been measured via neutron diffraction and similar residual stress trends in ceramics are observed. Also, from Fig. 2c) we can see that the residual stress in the joint without interlayer is larger than that in the joint with a Cu interlayer, which is larger than the residual stress in the joint with a Nb interlayer. The highest compressive residual stress values in the three joints are -157.7 MPa for the joint without any interlayer, -96.9 MPa for the joint with a Cu interlayer and -56.9 MPa for the joint with a Nb interlayer. This finding, for the first time, offers a direct proof that the residual stress distribution in the brazing joint could be moderated by applying different interlayer, which could have an important implication for developing new methods to reduce the residual stress in the ceramic/ metal brazing joint.

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Fig. 2.   a) An example of peak fitting, which shows the peak is well fitted using the Psdvoigt model, b) linear fitting between $\frac{d-d_0}{d_0}$ and sin²ψ showing a good linear fit between the two; c) residual stress as a function of depth in graphite/ copper brazing joint, which is generally compressive, increasing from the surface to the interface; the error bar is from the linear fitting from Fig. 2b); the black bar is the residual stress of the joint without any interlayers, the red bar shows the residual stress of the joint with the copper interlayer and the green bar represents the residual stress of the joint with Nb interlayer.

3.2. Microstructure and strength of the joint

As mentioned above, the graphite/ copper brazing joint comprises of very complex microstructure which could have a significant influence on the residual stress distribution in the joint. Thus, to understand the effect of the various interlayer on the residual stress distribution in graphite/copper brazing joints, the microstructure of the joints was observed by SEM and the results are shown in Fig. 3. The typical microstructure of the graphite/ copper brazing joint without any interlayers is demonstrated in Fig. 3a). It can be seen that reliable joining between graphite and copper is achieved by the AgCuTi brazing filler without any defects such as pores and cracks. The brazing filler has penetrated into graphite which has a porous microstructure, indicating good wettability of the brazing filler to the graphite. Since the surface of the copper substrate has been ground to 1 μm prior to brazing, the interface between it and the brazing filler is expected to be flat. However, as shown in Fig. 3a), the interface between the brazing filler and copper becomes rumpled. This indicates some interaction between the brazing filler and copper took place during the brazing procedure. From previous reports, Ag and Cu could dissolve with each other and form solid solutions. At elevated temperature, the copper substrate and the Ag based brazing filler will dissolve with each other and generate the rumpled interface between them. Grey phases with similar contrast to that of the copper substrate can be observed in the Ag matrix in the brazing seam, which should be the copper solid solution according to the previous report. To investigate the interaction between the graphite substrate and the brazing filler, the graphite/brazing filler interface is magnified and carefully observed, as shown in Fig. 3b). A very thin reaction layer with a thickness of less than 1 μm can be found adjacent to graphite. EDS was applied to characterise the composition of the various phases in the joint and the results are listed in Table 1. Table 1 illustrates that the matrix phase in the brazing seam with a brighter contrast is the Ag solid solution and the grey phase distributed in the Ag matrix is the copper solid solution. The ratio of Ti to C in the reaction layer adjacent to the graphite substrate is approximately 1, which infers that this reaction layer may be TiC. It needs to be noted that the dimension of the interaction volume of the electron beam in materials for SEM is usually larger than 1 μm. Thus this achieved composition of the reaction layer is an estimated result.

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Fig. 3.   Microstructure of the joints achieved without any interlayers, with a copper interlayer and with a niobium interlayer. a) The microstructure of the graphite/copper brazing joint without any interlayer, showing that the bonding between graphite and copper is successfully achieved using AgCuTi brazing filler; b) detailed microstructure of the interface between graphite and the brazing filler, showing a reaction layer formed adjacent to the graphite substrate, c) microstructure of the graphite/copper brazing joint with copper interlayer showing the copper interlayer has been dissolved by the brazing filler and the inserted figure demonstrates the detailed microstructure of the interface between graphite and the brazing filler, showing a reaction layer formed adjacent to the graphite substrate, d) microstructure of the graphite/copper brazing joint with Niobium interlayer, e) detailed microstructure of the brazing seam between graphite and the Niobium interlayer, from which a continuous layer adjacent to the Niobium interlayer can be found, f) detailed microstructure of the brazing seam between the Niobium interlayer and the copper substrate.

Fig. 3c) shows the microstructure of the joint achieved with a Cu interlayer, from which it can be seen that joining between graphite and copper is successfully achieved and the brazing filler fills up the pores in graphite as well. No continuous copper foil can be found inside the brazing seam indicating that part of the copper foil has been dissolved into the brazing filler and the brazing filler has penetrated into the copper foil. The width of the brazing seam has been increased from 20 μm to about 100 μm. The reaction layer adjacent to the graphite substrate still exists, as shown in the insert in Fig. 3c), demonstrating that the application of the copper foil will not affect the reaction between the brazing filler and graphite. When Nb foil is applied as the interlayer, the microstructure of the joint is altered, as shown in Fig. 3d). The whole brazing seam is divided into two parts by the Nb interlayer. The magnified image of the brazing seam on the graphite side is shown in Fig. 3e). It can be seen that, similar to the joint achieved without any interlayer and with copper interlayer, the reaction layer adjacent to the graphite still exists, which ensures the reliable bonding between the brazing filler and the graphite substrate. The brazing seam between the graphite and Nb interlayer mainly consists of Ag and Cu solid solutions. The interfacial microstructure near the Nb interlayer is different from that in the joint without any interlayer or the joint with a copper interlayer. A continuous layer with grey contrast can be found and some spotty phases with dark contrast distribute near the interface. EDS is used to investigate the composition of these two phases and the results are listed in Table 1. As can be seen from the table, the ration of Ti to Cu in the spotty phase with darker contrast is 1 and this phase is inferred to be TiCu. From the EDS result, the atom ratio between Nb and Cu in the continuous phase is approximately 1. Since there is no intermetallic between Cu and Nb and these two elements could dissolve with each other, this phase should be the Cu solid solution and Nb solid solution. Fig. 3f) shows the microstructure of the brazing seam on the copper substrate side. Some brazing filler has dissolved into the interlayer and some dark phase can be observed. From the EDS result shown in Table 1, these dark phases are determined to be Ti₂Cu, which is different from the observed TiCu phase in the brazing seam on the graphite substrate side. This may be because the reaction between the graphite and Ti consumes a certain amount of Ti, leaving less amount of Ti to react with Cu. As been measured above, the residual stress is highest in the graphite/copper joint without any interlayer, this may be explained by the fact that despite of the plastic deformation of the Ag solid solution, there are no other ways to reduce the residual stress in the joint. For the joint with a copper interlayer, some residual stress could be released through the plastic deformation of the ductile copper interlayer. Also, after applying this interlayer, the width of the brazing seam is increased, which benefits the deformation capability of the joint. Thus the residual stress in the joint with a copper interlayer is smaller than that in the joint without any interlayers. However, from Fig. 3c), it can be seen that brazing filler has diffused into the copper interlayer and makes it discontinuous. According to the previous report, the lost integrity of the interlayer can be detrimental to its function of releasing the residual stress in the joint. The Nb interlayer has a CTE of 7.3 × 10^-6 K^-1, which is between that of Graphite (6 × 10^-6 K^-1) and copper (16 × 10^-6 K^-1). The Nb foil in the joint could help form a gradient structure and moderate the residual stress distribution. At the same time, the Ag solid solution on both side of the Nb interlayer can also reduce the residual stress in the joint through plastic deformation, resulting in the conclusion that application of Nb interlayer is the most effective method to reduce the residual stress in graphite/copper joint in our experiments.

Since the residual stress is closely related to the strength of the joint, shear tests were carried out to investigate on the strength of the joint and the results are shown in Fig. 4a). It can be seen that when no interlayer is applied, the shear strength of the joint is only about 15 MPa. When the copper interlayer is used, the shear strength of the joint increases to about 30 MPa, while for the interlayer with a Nb interlayer, the shear strength is improved to about 45 MPa. Thus, the reduction of the residual stress in the joint could help improve the shear strength of the joint. The morphology of the fracture surface is observed by a digital optical microscope and shown in Fig. 4b). From Fig. 4b), we can see that the fracture of all the samples took place in the graphite substrate. As discussed above, the resolution of EDS for SEM may not be sufficient to investigate the composition of the reaction adjacent to the graphite substrate and CuK_α X-ray beam could penetrate through about 4.4 mm graphite. Thus XRD measurement is carried out on the fracture surface of the joint and the achieved pattern is refined using TOPAS. The results are shown in Fig. 4e-g). Since the footprint of the X-ray beam is larger than the graphite substrate, some copper peaks are picked in the pattern. And the copper plate is in rolling state, which consists of some texture. Thus Spherical Hamonics function of 4 orders is applied to model the texture in the copper plate. From Fig. 4e-g), it can be seen that the patterns are generally well refined and graphite, Ag, Cu and TiC phases can be indexed from the pattern, which helps confirm the EDS analysis result. It needs to be noted that the intensity of some peaks is not perfectly fitted. This may be explained by the fact that the surface of the fracture is not flat and thus the absorption of the X-ray at different 2theta angles is not the same, resulting in some peaks with abnormal intensity. Another interesting finding of the experiment is that the fracture positions of different joints are slightly different. For the joint without any interlayers and with Nb interlayer, the fracture took place near the interface, while for the joint with copper interlayer, the fracture happens about 1 mm further away from the interface than the other two joints. During the testing, the external loading will superimpose with the residual stress in the joint and lead to the final failure. Thus the joint tends to fail at the position where the highest residual stress locates. As shown in Fig. 2c), the highest residual stress in the joint without any interlayer and with Nb interlayer happen at the interface, while for the joint with copper interlayer, the highest residual stress locates about 1 mm further away from the interface than the other two kinds of joints, the position of which corresponds well with the fracture location. This could help explain the fracture of the joint with copper interlayer happens further away from the interface than the joint without any interlayer and the joint with the Nb interlayer.

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Fig. 4.   a) Shear strength of the joints showing that the residual stress in the joint with a Niobium interlayer is smaller than that of the joint with a copper interlayer, which is also smaller than the residual stress in the joint without any interlayer, b) fracture morphology of the joint without any interlayer, c) fracture morphology of the joint with a copper interlayer, d) fracture morphology of the joint with a Niobium interlayer, e) refinement result of the XRD pattern achieved on the fracture surface without any interlayer, f) refinement result of the XRD pattern achieved on the fracture surface with copper interlayer, g) refinement result of the XRD pattern achieved on the fracture surface with a niobium interlayer. The blue, black and the green lines are the original XRD pattern, the red line is the refined pattern and the grey line is the difference between the original pattern and the refined model, the small lines below show the refined Bragg peak positions.

4. Conclusion

The residual stress distribution as a function of depth in graphite/copper brazing joint is successfully measured by XRD. The residual stress in all the joints is found to be generally compressive, and the stress increases from the surface to the interface. The residual stress value in the joint without any interlayer is higher than the stress value in the joint with a copper interlayer, which is higher than that in the joint with a niobium interlayer. This indicates that both the copper and the niobium interlayers can reduce the residual stress in the joint and the niobium interlayer has a better effect. The brazing joint with a niobium interlayer has the highest strength of 45 MPa, and the strength of the joint with a copper interlayer is 30 MPa, which is higher than that of the joint without any interlayer (15 MPa). This result corresponds well with the measured residual stress value. The fracture position of the joint without any interlayer and with a niobium interlayer happens in the graphite substrate near the interface while for the joint with a copper interlayer, the fracture takes place about 1 mm away from the interface. The fracture position appears to be closely related to the highest residual stress in the joint.

Acknowledgements

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China under Grant Nos. 51805114 and U1737205 and China Postdoctoral Science Foundation under Grant No. 2018M631921.